List

Place Value, Integers, Ordering and Rounding - Short Problems

Highs and Lows
problem

Highs and Lows

Age
11 to 14
Challenge level
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What were the maximum and minimum temperatures recorded in my max/min thermometer?

Reverse ages
problem

Reverse Ages

Age
11 to 14
Challenge level
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When is the next time that Brian's age will be the reverse of his father's age?

Count Back
problem

Count Back

Age
11 to 14
Challenge level
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How well can you count back from sixty thousand?

Place value, integers, ordering and rounding - Short Problems
problem

Rough Rectangle

Age
11 to 14
Challenge level
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What is the smallest possible area that this rectangle could have?

Central Sum
problem

Central Sum

Age
11 to 14
Challenge level
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Can you find numbers between 100 and 999 that have a middle digit equal to the sum of the other two digits?

Negative Dice
problem

Negative Dice

Age
11 to 14
Challenge level
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If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Mini Kakuro
problem

Mini Kakuro

Age
11 to 14
Challenge level
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The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Debt Recovery
problem

Debt Recovery

Age
11 to 14
Challenge level
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Tony and Tina can't work out which of them owes what to the other. Can you?

Loose Change
problem

Loose Change

Age
11 to 14
Challenge level
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In how many ways can you give change for a ten pence piece?

Mathematical Ages
problem

Mathematical Ages

Age
11 to 14
Challenge level
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Arrange these three famous mathematicians in order with the shortest-lived first.

Quiz Questions
problem

Quiz Questions

Age
11 to 14
Challenge level
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Jack does a 20-question quiz. How many questions didn't he attempt?

Double with 1 to 9
problem

Double With 1 to 9

Age
11 to 14
Challenge level
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Can you find a number and its double using the digits $1$ to $9$ only once each?

Digital Book
problem

Digital Book

Age
11 to 14
Challenge level
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If it takes 852 digits to number all the pages of a book, what is the number of the last page?

Missing 9s
problem

Missing 9s

Age
11 to 14
Challenge level
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Sara makes a list of the whole numbers that do not contain any 9s. What is the 300th number on her list?

Tick Tock
problem

Tick Tock

Age
11 to 14
Challenge level
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Tick's watch is slow and Tock's watch is fast. How long is it before their watches differ by an hour?

Paying the Bill
problem

Paying the Bill

Age
11 to 14
Challenge level
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Gill and I went out to lunch. We agreed to split the total cost equally. How much did I owe Gill?

Even Squares
problem

Even Squares

Age
11 to 14
Challenge level
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Can you find squares within a number grid whose entries add up to an even total?

Digit Sum Puzzle
problem

Digit Sum Puzzle

Age
11 to 14
Challenge level
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Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?

Equal Length Powers
problem

Equal Length Powers

Age
14 to 16
Challenge level
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How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

Alberta's Age
problem

Alberta's Age

Age
14 to 16
Challenge level
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Alberta won't reveal her age. Can you work it out from these clues?

Repeat Product
problem

Repeat Product

Age
14 to 16
Challenge level
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Can you work out the value of P+Q+R in the multiplication shown?

Sum Up
problem

Sum Up

Age
14 to 16
Challenge level
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David listed ten consecutive numbers and removed one of them. Which number did he remove?

How many digits?
problem

How Many Digits?

Age
14 to 16
Challenge level
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How many digits are there in this product?

Pros and Cons
problem

Pros and Cons

Age
14 to 16
Challenge level
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If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

Digital Counter
problem

Digital Counter

Age
14 to 16
Challenge level
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When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?

Number Crunch
problem

Number Crunch

Age
14 to 16
Challenge level
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Create 24 numbers from four digits. Why is 101 always a factor of their sum?

How many gorillas?
problem

How Many Gorillas?

Age
14 to 16
Challenge level
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If the numbers in this news article have been estimated, then what is the largest number of gorillas that there could have been 10 years ago?

Place value, integers, ordering and rounding - Short Problems
problem

Digit Sum

Age
14 to 16
Challenge level
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What is the sum of all the digits in all the integers from one to one million?